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NovelinitializationschemeforFuzzyC-Meansalgorithmoncolorimagesegmentation

ArticleinAppliedSoftComputing·April2013

DOI:10.1016/j.asoc.2012.12.022

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Applied Soft Computing 13 (2013) 1832–1852

Contents lists available at SciVerse ScienceDirect

Applied Soft Computing

j ourna l ho me p age: www.elsev ier .com/ l ocate /asoc

ovel initialization scheme for Fuzzy C-Means algorithm on color imageegmentation

hang Siang Tan, Wei Hong Lim, Nor Ashidi Mat Isa ∗

maging and Intelligent Systems Research Team (ISRT), School of Electrical and Electronic Engineering, Engineering Campus, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang,alaysia

r t i c l e i n f o

rticle history:eceived 14 June 2012eceived in revised form 7 December 2012ccepted 30 December 2012vailable online 18 January 2013

a b s t r a c t

This paper presents a novel initialization scheme to determine the cluster number and obtain the initialcluster centers for Fuzzy C-Means (FCM) algorithm to segment any kind of color images, captured usingdifferent consumer electronic products or machine vision systems. The proposed initialization scheme,called Hierarchical Approach (HA), integrates the splitting and merging techniques to obtain the initial-

eywords:uzzy C-Means (FCM)ierarchical Approach (HA)

nitialization schemeplitting and merging

ization condition for FCM algorithm. Initially, the splitting technique is applied to split the color imageinto multiple homogeneous regions. Then, the merging technique is employed to obtain the reasonablecluster number for any kind of input images. In addition, the initial cluster centers for FCM algorithmare also obtained. Experimental results demonstrate the proposed HA initialization scheme substantiallyoutperforms other state-of-the-art initialization schemes by obtaining better initialization condition forFCM algorithm.

. Introduction

In digital image processing, image segmentation is a processf partitioning an image into non-overlapped, consistent regionshich are homogeneous with respect to some characteristics [1].

t serves as a critical and essential component of image analysisnd pattern recognition system because it determines the qual-ty of the final result of analysis [2]. Thus, it has been widelysed in many image analyses and pattern recognition applicationsuch as object recognition [3–5], optical character recognition [6,7],ace recognition [8], fingerprint recognition [9,10], medical imagerocessing [11,12], industrial automation [13] and content based

mage retrieval [14]. Due to its clustering validity and simplicityf implementation, FCM algorithm has long been a popular imageegmentation algorithm [15].

The FCM algorithm was introduced by Ruspini [16] and thenmproved by Dunn [17] and Bezdek [18]. It is a segmentationlgorithm that is based on the idea of finding cluster centers byteratively adjusting their position and evaluation of an objec-ive function. The iterative optimization of the FCM algorithm is

ssentially a local searching method, which is used to minimizehe distance among the image pixels in corresponding clustersnd maximize the distance between cluster centers. Its success

∗ Corresponding author. Tel.: +60 45996093; fax: +60 45941023.E-mail addresses: khangsiang85@hotmail.com (K.S. Tan),

imweihong87@yahoo.com (W.H. Lim), ashidi@eng.usm.my (N.A.M. Isa).

568-4946/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.asoc.2012.12.022

© 2013 Elsevier B.V. All rights reserved.

mainly attributes to the introduction of partial memberships forthe belongingness of each image pixel to all available clusters iden-tified by its centers. The partial membership is proportional to theprobability that a pixel belongs to a specific cluster where the prob-ability is only dependent on the distance between the pixel andeach cluster center. By iteratively adjusting the cluster centers, theobjective function of the FCM algorithm can reach the global min-imum when pixels nearly the center of corresponding cluster areassigned to higher membership while those far from the center ofcorresponding cluster are assigned lower membership.

However, the FCM algorithm is very sensitive to the initializa-tion condition of cluster number and initial cluster centers [19]. Theinitialization conditions of cluster number and initial cluster cen-ters have their impacts on the segmentation quality. For instance,the cluster number imposes significant impact on segment areawhereas the initial cluster centers affect the classification accuracyof the FCM algorithm as different selection of initial cluster centerscan potentially lead to different local optimal or different parti-tion. In general, to segment an image into F clusters, there are threemost popular initialization schemes as reported by Bezdek et al.[20], which can be described as follow:

1. Using F image pixels randomly selected from the image.2. Using the first F distinct image pixels in the image.

3. Using F image pixels uniformly distributed across the image.

Among these initialization schemes, using F image pixels ran-domly selected from the image as the initial cluster centers has

Compu

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K.S. Tan et al. / Applied Soft

een proven to be the best initialization scheme [21]. This initial-zation scheme is well known as randomly initialization scheme.

ang and Lu [22] proposed a new FCM variant with enhancedlgorithm’s speed and noise immunity. Accordingly, the algorithmsnitial cluster centroids could be extracted from the peak values ofmages’ gray histogram and this approach could reduce numberf iteration required by their algorithm to achieve the satisfactorylustering results. To increase the algorithm’s robustness towardhe noise signals (e.g. Gaussian noise, salt and pepper noise and

ixed noise), the local spatial information of images are incorpo-ated into their FCM variants. More specifically, a new objectiveunction is proposed to take both the neighbor mean and medianalues into account during the clustering of center pixels. Accord-ng to Guo et al. [23], neutrosophy [24] is a new powerful tool toescribe the image with uncertainty. Thus, they adopt the neutro-ophic set (NS) approach into the FCM technique to perform themage segmentation. In their proposed approach, the input imagesre first transformed into the NS domain, which is described byhree membership sets of white set (T), indeterminate set (I), andon-white set (F). A �-mean operation is performed on the NS

mages prior the FCM clustering process, in order to increase theniformity and homogeneity of NS images by reducing the NS’s

ndeterminacy. Motivated by the dependency of color clusteringesults on the color model and similarity functions used, Patrascu25] proposed a FCM variant that works based on a new measuref similarity. Accordingly, the new measure is defined in a newerceptual system of hsl and the clustering results based on thisew measure are promising. Despite achieving different improve-ents over the original FCM technique, the prior determination

f cluster numbers in these techniques is set manually by users.evertheless, the process of determining the cluster numbers is

aborious, especially for natural color images due to their com-lexity and diversity. Additionally, it is impractical to expect allsers to have sufficient domain knowledge in determining the accu-ate cluster numbers. As the initialization scheme has substantialmpact on the FCM’s clustering performance, wrong determina-ion of cluster numbers by users could deliver poor segmentationesults.

To alleviate the abovementioned drawback, an initializationcheme called Agglomerated Just Noticeable Difference HistogramAJNDH) was proposed to automatically determine the clusterumber and initial cluster centers with the aim to initialize theCM algorithm [26]. In this initialization scheme, the Just Notice-ble Difference (JND) histogram is first constructed to obtainnough number of histogram bins without compromising the visualmage content before applying the agglomeration to obtain thenitialization condition for FCM algorithm. With similar clusterumber, this initialization scheme was proven to be able to out-erform the randomly initialization scheme by obtaining better

nitial cluster centers and hence producing better segmentationesult.

In addition, Ant Colony Optimization (ACO) initializationcheme was also proposed to automatically obtain the initial-zation condition of cluster number and initial cluster centers tonitialize the FCM algorithm [27]. In this initialization scheme, anmproved Ant System (AS) includes a cluster merging step to auto-

atically keep a reasonable cluster number for all kinds of inputmages. In addition, the improved AS is also applied for intel-igent initialization of cluster centers. This initialization scheme

as also proven to be able to outperform the randomly initializa-ion scheme by obtaining better initial cluster centers and henceroducing better segmentation result, both with similar cluster

umber.

Chen et al. [28] proposed a FCM-based segmentation techniquey performing fusion on multi-color space components. Accord-

ngly, the input images are first transformed into the color spaces

ting 13 (2013) 1832–1852 1833

of grayscale, HSV, YIQ, YCvCr, LAB and LUV, respectively. A peak-finding algorithm is then applied on the components of gray, V, I,Cr, B, and U, from the corresponding color space to determine theirrespective initial cluster centroids and cluster numbers. The spatialFCM (SFCM) algorithm [29] is applied on these six selected com-ponents with different cluster numbers to generate six differentinitial segmentation results. A fusion process, implemented by theSFCM algorithm, is applied again on these six initial segmentationresults to obtain the final cluster number. Bahght et al. [30] pro-posed a new validity index to access the validity of a cluster. In theirapproach, a multi-degree entropy algorithm is proposed to per-form partition on the input image into different level of intensitiesusing the multi-degree immersion process. Based on the prede-fined validity function criteria, a merging process is applied on theoutput of aforementioned process to obtain the image’s final clusternumbers. Meanwhile, Sowmya and Sheela Rani [31] investigate thecapability of FCM, Possibilistic FCM (PFCM) [32], and competitiveneural network [33] in performing the image segmentation. In theirstudies, a self-estimation algorithm proposed in [34] is adopted toautomatically determine the cluster numbers.

In this paper, we propose a novel initialization scheme calledHierarchical Approach (HA) to automatically determine the clusternumber and to obtain the initial cluster centers, which are used toinitialize the FCM algorithm. In the proposed initialization scheme,the color image is split hierarchically into multiple homogeneousregions before merging is carried out to obtain the initializationcondition for the FCM algorithm.

The rest of the paper is organized as follows: Section 2 presentsthe working of FCM algorithm. Section 3 will describe the proposedinitialization scheme. Section 4 will analyze the segmentationresults produced by the FCM algorithm using the proposed initial-ization scheme and at the same time comparing it with those usingother initialization schemes. Finally, Section 5 concludes the workof this paper.

2. Fuzzy C-Means algorithm

FCM algorithm is an unsupervised classification technique, thusthere is no need for prior knowledge about the pixels set. It is asegmentation algorithm that is based on clustering similar pixelsin an iterative way where the cluster centers are adjusted duringthe iteration. It attempts to partition the pixels into a collection of Ffuzzy clusters. Based on the minimization of the objective function,the conventional FCM algorithm yields extremely good segmenta-tion results. Typically, the objective function of the conventionalFCM algorithm is defined as:

W (q) =F∑

j=1

N∑i=1

umij ||xi − cj||2 (1)

where N is the number of image pixels, �ij is the membership ofpixel xi to the jth cluster identified by its center cj, and m is a con-stant that defines the fuzziness of the resulting partition. ||xi − cj||denotes the Euclidean distance between xi and cj. The parameter mcontrols the fuzziness of the membership. The value of m is manu-ally determined by the user. In general, most users choose m in therange [1.5, 2.5], with m = 2.0 being an overwhelming favorite. Themembership of pixel xi to the jth cluster identified by its center cjis defined as:

uij =F∑

k=1

( ||xi − cj||||xi − ck||

)−2/m−1

(2)

1 Compu

wcc

c

b0

3

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cmc

834 K.S. Tan et al. / Applied Soft

here �ij indicates the strength of the association between xi andj and has the value in the range [0, 1]. In FCM algorithm, the clusterenters are iteratively updated as:

j =∑N

i=1umij

xi∑Ni=1um

ij

(3)

The procedure of FCM algorithm is illustrated in Fig. 1 as follow:(Notes: ε is a constant and its value is manually determined

y the user. In general, most users choose ε in the range of [0.01,.0001], with ε = 0.001 being an overwhelming favorite.)

. Proposed Hierarchical Approach

Earlier studies reveal that FCM clustering results are highlyependent on the initializations of the cluster centers and numberf clusters. A good initialization conditions can only be obtainedy running repetitive experiments based on certain experiences, ifhere is no initialization scheme that can automatically determineoth the cluster numbers and centers. Nevertheless, this approach

s laborious and the clustering results obtained are not alwaysromising.

In this study, we proposed the HA module as an initializationcheme for the FCM technique. In other words, the HA mod-le allows users to automatically and adaptively determine bothhe cluster numbers and centroids, which serves as the initializa-ion conditions for the FCM technique. Compared with the widelysed random initialization scheme, the HA module requires a less

aborious process and consistently produces good initializationonditions for the FCM technique. The capability of the HA mod-le to determine cluster numbers and centroids automatically anddaptively is due to ability of the HA module to detect them basedn the global information in the histogram of the input images.ifferent types of input images have different types of global infor-ation. Therefore, the HA module eventually detects different

luster numbers and centroids, depending on the numbers andntensity values of the significant peaks that are present in theistograms of the input images.

The proposed Hierarchical Approach (HA) initialization schemeonsists of two modules namely the splitting module and theerging module. The splitting module is employed to split the

olor image into multiple small homogeneous regions whereas the

FCM Alg orith m

1: Initialize the fuzzy clus ter nu mber , F and

Set iteration time q = 0 ;

2: whil e )1()( qq WW do

3: for j = 1 to Fth cluste r do

4: fo r i = 1 to Nth image pix el do

5: Calc ula te ij , i.e. the membe

(r epresen ted by jc ), using E

6: if 0ji cx then

7: 1ij ;

8: reset other mem bership

9: end if

10: end fo r

11: Update jc acco rding to Equa tio

12: end fo r

13: Ca lculate objecti ve functi on )(qW u

14: 1qq ;

15: end whil e

Fig. 1. Implementation of

ting 13 (2013) 1832–1852

merging module is applied to merge those regions that are percep-tually close to each other to determine cluster number and to obtainthe initial cluster centers for FCM algorithm. Each of the modulesis presented in the following sections respectively.

3.1. Splitting module

Previous literatures [35–37] revealed that both of the color spaceand the similarity/dissimilarity function used to measure the colorseparation/differences play significant roles in the image analysis’sresults. Although the RGB color space is widely used to representthe image data in image processing research, it is not a percep-tually uniform color space and thus incapable to model the wayin which humans perceive color. More specifically, the color differ-ences obtained (i.e. Euclidean distance) from the three dimensional(3-D) RGB color space do not correspond to the human perceptionof such differences [38,39]. This inhibits the application of RGB colorspace in various image processing tasks.

Being an approximately uniform color space, HSI achieves bet-ter approximation of human perception on the color differences, ascompared to the RGB color space [39]. In color images, HSI colorspace separates the color information (represented by Hue andSaturation) from its intensity information. In HSI, Hue representsbasic colors and is determined by the dominant wavelength in thespectral distribution of light wavelengths. Saturation is a measureof the purity of the color and signifies the amount of white lightmixed with Hue. Intensity is a measure of the image brightnessand is determined by the amount of light. In general, there are twopopular variants of HSI color space, namely the HSL and HSV colorspaces. The HSI color space has been used extensively for imageprocessing [40–42] due to their intuitive appeal to human’s per-ception and their provision for isolating the luminance component[41]. Thorough experimental studies have been presented in [39]to measure the impact of the use of different color spaces on theperformance of color texture analysis methods such as segmenta-tion or classification. It is reported that the approximately uniformspace of HSI outperforms the perceptually non-uniform RGB spacein both the noise-free and noisy conditions, suggesting that the HSI

could be a superior color space compared to RGB for image analysis[39].

Despite having significant advantages over the RGB space, theconventional HSI space encounters some undesirable issue that

the cluster centers, },...,...,{ 1 Fj cccc .

rs hip of pixel ix to the jth cluster

quation (2) ;

of pixel i to 0 ;

n (3) ;

sing Equa tion (1) ;

the FCM algorithm.

K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852 1835

d as p

lrmwori[ind

H

S

L

Hgtc

cttcgervfbe

Fig. 2. Possible scenario for intensity level i to be identifie

imits its application in image processing task. Recall that the Satu-ation in both the HSL and HSV spaces represents percentages of theaximum saturation obtainable for a given lightness [43]. In otherords, for the case where Saturation range is small, large variation

f Intensity ranges could be observed and this leads to the occur-ence of some undesirable artifacts (e.g. noise) in the Saturationmage [43]. To encounter the aforementioned drawback, Hanbury43] proposes to remove the saturation normalization by lightnessn HSI space, thereby derives a unified model of cylindrical coordi-ate HSL color space, where the Hue, Saturation and Lightness areefined respectively as [43]:

= arctan

( √3(G − B)

2R − G − B

)(4)

= max(R, G, B) − min(R, G, B) (5)

= R + G + B

3(6)

In this study, we adopt the new HSL color space proposed byanbury [43] to hierarchically split the color image, backed by itsood approximation on the human’s color perception (comparedo RGB space) and its achievement in overcoming the drawback ofonventional HSI space.

In the proposed HA initialization scheme, the splitting moduleonsists of 3 phases. In each phase, a peak finding algorithm, namelyhe Peak Finding Histogram Analysis (PFHA) algorithm, is proposedo obtain the modes in the histogram before the valleys can be suc-essfully identified. For the histogram analysis, the histogram ofray scale image can be separated into several numbers of modes,ach corresponds to one region, and there is a threshold value cor-esponding to the valley between two adjacent modes [44]. The

alley between two adjacent modes can be used as the boundaryor gray scale image segmentation. In the PFHA algorithm, at theeginning, a moving average filter is applied to remove the unnec-ssary peaks and valleys in the histogram. It is done by taking the

Fig. 3. Possible scenario for intensity level i to be identified as v

eak by Eq. (8), (a) h (i–1) > h (i+1) and (b) h (i–1) < h (i+1).

average number of pixels among the 2L + 1 (where L is a positiveinteger number) adjacent discrete levels in the histogram as:

h(i) = [n(i − L) + n(i − (L − 1)) + . . . + n(i) + . . . + n(i + (L − 1)) + n(i + L)]2L + 1

(7)

where n(i) is the number of pixels associated with ith level in thehistogram and h(i) is the value of ith level after applying the movingaverage.

(Note: In this study, the span of the moving average filter canbe set from 2 to 8, based on the analysis done using numerousimages. However, the span of the moving filter that is smaller than2 is not capable to eliminate the non-significant peaks reside in thehistogram of each color channel respectively. Meanwhile, the spanof the moving average filter that is larger than 8 could potentiallyremove certain significant peaks reside in the histogram of eachcolor channel respectively, which is not desirable. Thus, we set thespan of the moving average filter as 5, by taking the average valuebetween these two extreme values.)

Despite the smoothing process performed by the moving aver-age filter, there are still some insignificant peaks and valleysdetected in the new histogram and they are identified by Eqs. (8)and (9), respectively. The possible scenarios for a given intensitylevel i to be identified as the peak and valley are illustrated inFigs. 2 and 3 respectively.

Peak = (i, h(i)|h(i) > h(i − 1)&h(i) > h(i + 1)) (8)

Valley = (i, h(i)|h(i) < h(i − 1)&h(i) < h(i + 1)) (9)

To remove all these insignificant detected peaks and valleys, wepropose a set of IF-THEN rule base, represented by Eqs. 10(a)–10(d).Generally speaking, if a particular intensity level of i is identifiedas peak (i.e. Fig. 2), we first examine the average pixel numbersof its two nearest neighbor, i.e. h (i − 1) and h (i + 1). To remove

the insignificant peak that contributed by i, we replace the averagepixel numbers of i, i.e. h (i), with h (i − 1) or h (i + 1), whicheverhas the larger value. For intensity level of i that identified as valley(i.e. Fig. 3), we replace h (i) with h (i − 1) or h (i + 1), whichever has

alley by Eq. (9), (a) h (i–1) > h (i+1) and (b) h (i–1) < h (i+1).

1836 K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852

y (a) E

tcri

pi

Fig. 4. Illustration of the removal of insignificant peak and valley b

he smaller value, in order to remove the insignificant valley thatontributed by i. Fig. 4 illustrates the mechanisms of Eq. (10) inemoving the insignificant peak and valley that contributed by thentensity level i.

IF(i ∈ Peak)AND(h(i + 1) > h(i − 1))

THEN(h(i) = h(i + 1))(10a)

IF(i ∈ Peak)AND(h(i + 1) < h(i − 1))

THEN(h(i) = h(i − 1))(10b)

IF(i ∈ Valley)AND(h(i + 1) < h(i − 1))

THEN(h(i) = h(i + 1))(10c)

IF(i ∈ Valley)AND(h(i + 1) > h(i − 1))(10d)

THEN(h(i) = h(i − 1))

As a result, a new smoothed histogram, without any insignificanteaks and valleys, could be obtained. In order to obtain the modes

n the new histogram, we first examine the gradient change, grad

q. (10a), (b) Eq. (10b), (c) Eq. (10c), and (d) Eq. (10d), respectively.

(i) exhibited by each intensity level i in the new histogram. Math-ematically, grad (i) represents the variation of h (i) to h (i + 1) withrespect to the intensity level i and it is represented as follows:

grad(i) = h(i) − h(i − 1) (11)

By successively examining the grad (i) values of each intensitylevel i, we could identify the intensity level i as mode in the newhistogram, if the conditions of h (i) > h (i − 1) and h (i + 1) < h (i) arefulfilled. In other words, the intensity level i in the new histogramis assigned as the modes, if the grad (i) shows positive value (i.e.h (i) > h (i − 1)), whilst the grad (i + 1) shows negative value (i.e. h(i + 1) < h (i)). Mathematically, the modes identification mechanismis represented as follows:

Mode = (i, grad(i)∣∣grad(i) ≥ 0 &grad(i + 1) < 0) (12)

After the modes in the new histogram are detected, the val-leys can be obtained by taking the minimum value between anytwo adjacent modes in the new histogram. They are used as the

K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852 1837

PFHA Al gorithm

1: Apply a moving aver age filter on the input his togram to remove the un nece ssary

peaks and valle ys using Equat ion (7) ;

2: Identify insignifica nt pea ks and valley using Equat ions (8) and (9) respect ively ;

3: Remove insignif icant peaks and val ley in new histogram using Equat ions (10) ;

4: Identify modes in new smoothed histogr am using Equat ions (1 1) and (12) ;

5: Ident ify valleys in new smoothed histogram by taking mi nimum value betw een

bm

tfgdvtasruaouurrnoihaHtc

c

wi

Ptttsaibtifs

3

uicio

M

Table 1Categories of color similarity in terms of the Manhattan distance [45].

dc Visual inspection result

10–30 Same color31–70 Same color, low intensity variance71–90 Same color series91–120 Same color series, low intensity variance121–150 Different colors, small color range

any ad jace nt modes in the hi stogram ;

Fig. 5. Implementation of the PFHA algorithm.

oundaries for segmentation in this paper. Generally, the imple-entation of the PFHA algorithm is illustrated in Fig. 5 as follows:In the first phase of the proposed HA initialization scheme (i.e.

he splitting module), 3 steps are involved. First, Hue histogramor all the image pixels is constructed as Hue can be easily distin-uished, while the perception of different Saturation and Lightnessoes not imply the recognition of different colors in the humanision system. Then, the proposed PFHA algorithm is used to locatehe modes in the histogram. Finally, the valleys can be obtainedfter the modes are located and they are used as the boundaries foregmentation. Although each region obtained is homogeneous withespect to Hue, the pixels of each region may consist of different Sat-ration as Hue is invariant to certain types of highlights, shadingnd shadows. Thus, for all the regions obtained in the first phasef splitting module, 3 steps involved in the first phase are againsed in Saturation histogram in the second phase of splitting mod-le. Thus, the regions are further split into multiple homogenousegions with respect to both Hue and Saturation. However, theseesultant regions play little role in distinguish colors if the Light-ess of the color lies close to black or white. Thus, for all the regionsbtained in the second phase of splitting module, 3 steps involvedn the first phase of splitting module are again used in Lightnessistogram in the third phase of splitting module. Thus, the regionsre further split into multiple homogenous regions with respect toue, Saturation and Lightness. The resultant regions obtained after

he third phase of splitting module are represented by its respectiveluster center. The cluster centers are obtained as:

j = 1|Rj|

∑xi ∈ Rj

xi (13)

here Rj is the pixel set that are assigned to jth cluster center, |Rj|s the number of pixels assigned to jth cluster.

It is worth mentioning that, our main purpose to employ theFHA algorithm on Hue, Saturation, and Lightness’s histograms iso identify the significant peaks and valleys on these histograms,hereby obtain the boundaries for segmentation. It is evidenthat output images produced by the PFHA algorithm consist ofmoothed histograms of Hue, Saturation, and Lightness, due to theveraging process (i.e. Eq. (7)), as well as the elimination of insignif-cant peaks and valley (i.e. Eqs. (8)–(10)). However, reader shoulde aware that such smoothed images will not be employed forhe further processing. To prevent the blurring effect on the inputmages, we apply both of the significant peaks and valleys, obtainedrom the PFHA algorithm, on the original images for the subsequentteps.

.2. Merging module

The number of cluster formed by the homogeneous regions issually large and is not suitable for post-processing, especially in

mage segmentation by the FCM algorithm. To obtain reasonableluster number to initialize the FCM algorithm, a merging technique

s applied to merge the clusters that are perceptually close to eachther.

In the merging technique, there are 2 steps involved. First, theanhattan distance between any two cluster centers, Dshortest is

151–190 Different colors, wider color rangeAbove 190 Very randomly occurring color

computed. The employment of the Manhattan distance to measurethe color similarity between any two cluster centers is motivatedby the experimental findings reported by Loo and Tan [45]. Accord-ingly, Manhattan distance is a better distance measurement thanthe Euclidean distance as the former exhibit a more stable visualcolor similarity, whilst the latter tends to produce wider variationof color perception with the same color distance [45].

The two nearest clusters are then merged and the new clustercenters are updated by Eq. (13) if their Manhattan distance, is lessthan predefined threshold, dc. As shown in Table 1, Loo and Tan[45] revealed that the Manhattan distance is below 70, where thesame color is observed with a very low intensity variance. Thus, weset dc to be 70 to merge the perceptually close cluster centers.

In the merging technique, these steps are repeated until no min-imum Manhattan distance between two nearest cluster centers isless than the predefined threshold dc. As a result, the cluster num-ber and the initial cluster centers could be obtained for the FCMalgorithm. The implementation of the merging module is presentedin Fig. 6.

3.3. Illustration of the implementation procedure

In order to provide the clear understanding of the fundamen-tal concept of the proposed HA initialization scheme, we presentthe implementation illustration of the proposed HA initializationscheme in detail in this section. The test image House as shownin Fig. 7(a) is adopted for the implementation illustration of theproposed HA initialization scheme.

As explained in the previous section, the HA initializationscheme consists of three phases to hierarchically split the testimage House into multiple homogenous regions in the HSL colorspace. In the first phase of the HA initialization scheme, the Huehistogram of the test image House will be computed, and then fol-lowed by the application of the PFHA algorithm to locate the modesin the histogram. The valleys between the two adjacent modes inthe Hue histogram will be used as the segmentation boundariesin the first phase of the HA initialization scheme. The segmentedresult after the first phase of the HA initialization scheme, whichconsists of 15 types of clusters is shown in Fig. 7(b). In this figure, itis clearly seen that the edge of the house roof has been mistakenlyassigned to be part of the sky due to the reason that Hue is invariantto highlights, shadings, and shadows.

In order to form the regions that are variant to highlights, shad-ings, and shadows, the Saturation histogram for every regionsobtained in the first phase of the HA initialization scheme is com-puted. In this second phase of the HA initialization scheme, thePFHA algorithm is again applied to obtain the modes and valleysof the Saturation histogram. The segmented result after the secondphase of the HA initialization scheme, which consists of 44 types ofclusters is shown in Fig. 7(c). It can clearly be observed that, unlikethe segmented results produced during the first phase of the HA

initialization scheme, the regions obtained in the second phase aredistinguishable to highlights, shadings, and shadows.

Despite the fact that the segmented results produced in the sec-ond phase are distinguishable to highlights, shadings, and shadows,

1838 K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852

Merging Module

1: Calc ulate all the M cluste r cente rs for all the r egions obta ined afte r the third p hase

of Splitti ng Mo dule using Equation (13) ;

2: whil e dcDsho rtest do

3: Ca lcu late the Ma nhattan distance, D bet ween any two out of the M cluster

centers ;

4: Identify the shortest dista nce betwee n two nea rest cluste r ce nte rs, shortestD ;

5: Merge the two neare st clu sters ;

6: Refresh the ov erall clus ter c enters us ing Equation (13) ;

7: Re duce the cluster numbe r M by one ;

8: end whil e

Fig. 6. Implementation of the merging module.

Fig. 7. Illustration of segmentation result using the proposed HA initialization scheme: (a) test image House, (b) segmented result after first phase, (c) segmented result aftersecond phase, (d) segmented result after third phase, (e) segmented result after merging process and (f) final segmentation result.

K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852 1839

, (a) p

yipesPhros

ttintcrs

4

PAp(aacsp

Fig. 8. The peaks and valleys located on the histogram for image House

et they still play insignificant role in distinguishing regions if thentensity of the regions lie close to white or black. Thus, in the thirdhase of the HA initialization scheme, the Lightness histogram forvery regions obtained in the second phase of the HA initializationcheme are constructed. Similar to the first and second phases, theFHA algorithm is applied again to locate the modes in the Lightnessistograms, followed by the identification of the valleys in the cor-esponding histograms. The segmented result after the third phasef the HA initialization scheme consists of 101 types of clusters ashown in Fig. 7(d).

In order to obtain the reasonable number of cluster used to ini-ialize the classical FCM algorithms, a merging process is employedo merge the similar regions. The segmented result after the merg-ng process consists of 9 types of clusters as shown in Fig. 7(e). Theumber of cluster and their corresponding centers obtained afterhe merging process are used as the initialization condition for theonventional FCM algorithm. Finally, the conventional FCM algo-ithm is applied to perform color image segmentation and the finalegmented result is illustrated in Fig. 7(f).

. Results and discussion

This section begins with the investigation of the proposedFHA algorithm’s capability in detecting the histograms’ modes.s explained in the previous section, it can be observed that pro-osed PFHA algorithm has played a vital role in locating the modesrepresenting the homogenous regions) of the Hue, Saturation,nd Lightness histograms. The performance of the proposed PFHA

lgorithm has huge impact on the clustering quality as the finalluster number produced is greatly dependent on the number ofignificant modes identified in the early stage. Thus, in the firstart of this section, we are particularly interested to evaluate the

Fig. 9. The peaks and valleys located on the histogram for image Mountain, (a)

eaks located on its histogram and (b) valleys located on its histogram.

capability of the proposed PFHA algorithm in identifying and locat-ing the modes of the histogram. A total of 100 grayscale images,taken from the public segmentation database are adopted to eval-uate the capability of the proposed PFHA algorithm.

On the other hand, for the second part of this section, theperformance of the proposed HA initialization scheme will becompared with the randomly initialization scheme, and severallatest adaptive initialization schemes, namely the Ant Colony Opti-mization (ACO) and the Agglomerated Just Noticeable DifferenceHistogram (AJNDH) initialization schemes. The randomly initial-ization scheme is chosen for the performance comparison as it hassuccessfully proven its outstanding performance over the other twoinitialization techniques as reported by Bezdek et al. [20], amongthe C-means family [21]. As the randomly initialization schemecould not decide the number of cluster for each image adaptively,we assign the number of cluster of the randomly initializationscheme with the final cluster number obtained from the HA ini-tialization scheme for the purpose of fair comparison.

For the ACO initialization scheme, it applies the intelligentsearching capability of the Ant Colony Algorithm (ACA) to auto-matically determine the number of cluster and their correspondingcluster centers, which are required in the subsequence stage ofthe FCM algorithm. The ACO initialization scheme is chosen forthe comparison as the previous literature [27] has demonstratedits excellent performances over the other recently proposed tech-niques such as the X-means, Mean Shift, Normalized Cut, and Hanand Shi’s methods. Meanwhile, the AJNDH initialization scheme,which is one of the latest introduced initialization schemes, is also

chosen for comparisons as we are interested to see whether ourproposed HA initialization scheme could generally outperform theAJNDH initialization scheme. In the second part of this section, atotal of 140 color images obtained from the public segmentation

peaks located on its histogram and (b) valleys located on its histogram.

1840 K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852

h, (a) p

dpi

4

MbtphamB

haeHmFtomortmc

Fig. 10. The peaks and valleys located on the histogram for image Beac

atabases are used as tested dataset for the performance com-arison between the proposed HA and other state-of-the-art

nitialization schemes.

.1. Evaluation on the proposed PFHA algorithm

In this subsection, three grayscale test images namely House,ountain and Beach are evaluated in details to highlight the capa-

ility of the proposed PFHA algorithm in identifying and locatinghe modes in the histogram. Generally, as shown in Figs. 8–10, theroposed PFHA algorithm can successfully locate the modes in theistograms and then the valleys (i.e. minimum value between twodjacent modes) on the histograms can be found. These values ofodes and valleys for the grayscale images of House, Mountain and

each are shown in Figs. 8(a), (b)–10(a), (b), respectively.In this study, the valleys between two adjacent modes on the

istograms have been proven to play a significant role, i.e. useds boundaries for the segmentation as shown in Figs. 11–13. Forxample, based on this concept, notice for the grayscale imageouse, the sky as well as the wall of the house are successfully seg-ented as homogeneous regions respectively as shown in Fig. 11.

or the grayscale image Mountain as illustrated in Fig. 12, the moun-ains are successfully separated as different clusters and we couldbserve the different layers of mountains as shown in the seg-ented image. Similarly, for the grayscale image of Beach, both

f the beach and sky are segmented as two different homogenous

egions as shown in Fig. 13. These promising results obtained showhat the proposed PFHA algorithm could successfully locate the

odes in the histogram and the valleys identified in the next stageould play a significant role in segmenting the input images into the

Fig. 11. Result on segmentation for image House, (a) or

eaks located on its histogram and (b) valleys located on its histogram.

homogeneous regions of interest. As a result, we conclude that theproposed PFHA algorithm could be applied in the splitting moduleof the proposed HA initialization scheme to split any input colorimages into the multiple homogenous regions.

4.2. Performance comparison with unsupervised initializationschemes

As mentioned previously, the proposed HA initialization schemewill be compared with the randomly initialization scheme and sev-eral latest adaptive unsupervised initialization scheme, namely theACO and AJNDH initialization schemes. In this section, the segmen-tation results produced by the randomly initialized, ACO, AJNDH,and HA initialization schemes are first evaluated qualitatively, i.e.through the naked eye, in term of the homogeneity of the seg-mented areas. In addition, the accuracy of the classification will beused to visually evaluate the performance of these algorithms asit is affected by the initial cluster centers. Meanwhile, as the con-ventional FCM algorithm is very sensitive to the cluster numberproduced in the initialization stage, it is worth to evaluate and dis-cuss the capability of the abovementioned initialization schemesin producing the cluster number as each of these initializationschemes are able to initialize the cluster centers distribution adap-tively.

In addition, we are also interested to investigate the clusterquality produced by the randomly initialized, ACO, AJNDH, and HA

initialization schemes as the final segmentation results in our workis significantly dependant on the cluster quality. Several importantcluster validity criteria have been featured by the previous work onthe fuzzy clustering for the evaluation of the cluster quality. In this

iginal image and (b) resultant segmented image.

K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852 1841

n, (a)

ptq

M

wnotiMtdg

eAmcrt

Fig. 12. Result on segmentation for image Mountai

aper, we adopt the mean square error (MSE) analysis to serve ashe benchmark function that could be used to evaluate the clusteruality, which is described as follow:

SE = 1N

M∑j=1

∑i ∈ Si

||xi − cj||2 (14)

here N represents the number of output image pixels and M is theumber of cluster produced during the clustering process. On thether hand, Sj represents the set of pixels in jth cluster, cj denoteshe pixel’s intensity levels of the jth cluster center, and xi is thentensity levels of ith pixel in jth cluster center. The concept of the

SE analysis is quite simple: for a fixed number of cluster, the clus-er centers should be placed in such a way that they reduce theistance to data pieces as much as possible, in order to generate aood clustering results, which has small distortion.

Finally, a total of three benchmark analyses will be used tovalute the segmentation results of the randomly initialized, ACO,JNDH, and HA initialization schemes quantitatively. These bench-

ark analyses are chosen as the standard quantiative tests for

olor segmentation to evaluate the goodness of the segmentationesults based on some human characterization about the proper-ies of ideal segmentation [27,46]. All of these three benchmark

Fig. 13. Result on segmentation for image Beach, (a) or

original image and (b) resultant segmented image.

functions are used to penalize the segmentation that form too manyregions and having non-homogenous regions by giving a largervalues. These three benchmark function are described as follows:

F(I) proposed by Liu and Yang [47],

F(I) =√

M∑M

j=1e2j√

Nj

(15)

F′(I) proposed by Borsotti et al. [48],

F ′(I) =∑M

j=1e2j

√∑MaxAreaa=1 [S(a)]1+1/a

(1000 × N)√

Nj

(16)

Q(I) further refined from F(I) by Borsotti et al. [48],

Q (I) =√

M

1000 × N

M∑j=1

[e2

j

1 + log Nj+

(S(Nj)

Nj

)2]

(17)

where I is an image and N is the total pixels in I. The segmentationcan be described as an assignment of pixels in the image I into M

regions. Let Cj denotes the set of pixels in region j, Nj = |Cj| denotesthe number of pixels in Cj. The value of ej, which represents thehomogeneity within a region, is defined as the Euclidean distancesbetween the RGB color vectors of the pixels of region j and the color

iginal image and (b) resultant segmented image.

1842 K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852

F of thA

vdeintfoi

4

stiCitttttIsc

crsutcptimr

ig. 14. The image House; (a) original image, and the rest are segmentation resultsJNDH, and (e) HA.

ector attributed to region j in the segmented image. Finally, S(a)enotes the number of regions in the image I that has an area ofxactly a and MaxArea denotes the largest region in the segmentedmage. It is worth to point out that these evaluation functions doot require any prior knowledge of correct segmentation. Hence,he users do not need to set any parameter or threshold valuesor the quantitative evaluation of the segmentation performancen color images. In these evaluation functions, the smaller valuendicates the better segmentation result.

.2.1. Qualitative evaluation on segmentation resultsIn this section, the results of the proposed HA initialization

cheme and the randomly initialized, ACO, and AJNDH initializa-ion schemes are evaluated visually using 7 out of the 140 testedmages. The segmentation results for those images, namely House,apsicums, Nemo, Fire Fighter, Birds, Swimmer, and Moon are shown

n Figs. 14–20, respectively. Generally, the proposed HA initializa-ion scheme produces better segmentation results as compared tohe other compared initialization schemes for all images as illus-rated in Figs. 14–20. The proposed HA initialization scheme is ableo produce more homogeneous segmented regions as compared tohe randomly initialized, ACO, and AJNDH initialization schemes.n addition, the proposed HA initialization scheme also achievesuperior performance in preserving the salient features of the inputolor images as it possess an excellent accuracy of classification.

As for image House illustrated in Fig. 14, there is an obviouslassification error in the segmentation results produced by theandomly initialized, ACO, and AJNDH initialization schemes ashown in Fig. 14(b)–(d), respectively by mistakenly assigned theppermost line in purple color as part of the house. However,he proposed HA initialization scheme successfully prevents thislassification error from occuring and manages to segment theurple line to be a single region as shown in Fig. 14(e). In addi-

ion, the HA initilization scheme also outperforms the randomlynitialized, ACO, and AJNDH initialization schemes by producing

ore homogenous house roof and wall as shown in Fig. 14(b)–(e),espectively.

e test image by various initialization schemes (b) randomly initialized (c) ACO, (d)

Similarly, for the image Capsicums as illustrated in Fig. 15,the proposed HA initialization scheme also produces better seg-mentation results than the randomly initialized, ACO, and AJNDHinitialization schemes. This is because the proposed HA initializa-tion scheme is capable to produce a significantly more homogenoussegmented regions on the red capsicum’s and the green capsicum’ssurfaces as compared to the other initialization schemes. As forimage Nemo shown in Fig. 16, it is interesting to see that there isan classification error where the body of Nemo fish is mistakenlyassigned to the background by the randomly initialized and ACOinitialization schemes as shown in Fig. 16(b) and (c), respectively.Both of the AJNDH and HA initialization schemes, however, havesuccessfully avoided this classification error by clustering the Nemofish’s body and the background into two distintive clusters. Further-more, the proposed HA initialization scheme successfully provesits superior performance over the AJNDH initialization scheme byproducing a more homogenoues region on the Nemo fish’s body asillustrated in Fig. 16(e) and (d), respectively.

Notice for the image Fire Fighter as shown in Fig. 17, the ran-domly initialized, AJNDH, and HA initialization schemes producebetter segmentation results than the ACO initialization schemeby assigning the helmet of the fire fighter into the desired bluecolor. Although the randomly initialized and AJNDH initializationschemes do not suffer the severe classification error as demon-strated by the ACO initialization scheme in Fig. 17(c), there areconsiderable number of pixels in the blue helmet are falselyassigned as the background as can be seen in the resultant imagesproduced by the randomly initialized and AJNDH initializationschemes in Fig. 17(b) and (d), respectively. In addition, for theresultant segmented image produced by the AJNDH initializationscheme as shown in Fig. 17(d), some pixels in the yellow color stripare falsely clustered as the part of the orange color uniform. Whileall the compared initialization schemes have demonstated different

level of classification errors, the proposed HA initialization scheme,on the other hand, has successfully avoided these classificationerrors by assigning the blue helmet, background, orange uniform,and yellow strip as separate clusters as shown in Fig. 17(e). This

K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852 1843

F ults o(

oHc

aAcwFi

FA

ig. 15. The image Capsicums; (a) original image, and the rest are segmentation resd) AJNDH, and (e) HA.

bservation again proves the superior accuracy of the proposedA initialization scheme in classifying the objects into differentlusters of interest.

For the image Birds as shown in Fig. 18, it can be observed thatll the segmented images produced by the randomly initialized,CO, and AJNDH initialization schemes are experiencing a severe

lassification error as all of these techniques mistakenly assign thehite feather of the bird into the blue color sky as illustrated in

ig. 18(b)–(d), respectively. Despite the fact that the HA initial-zation scheme produces more clusters at the background, it has

ig. 16. The image Nemo; (a) original image, and the rest are segmentation results of theJNDH, and (e) HA.

f the test image by various initialization schemes (b) randomly initialized (c) ACO,

successfully avoided the abovementioned classification error byassigning the white feather of bird and blue color of sky into twodifferent clusters as shown in Fig. 18(e). Meanwhile, for imageSwimmer as illustrated in Fig. 19, we could observe that both ofthe randomly initialized and ACO initialization schemes fail to clas-sify the pixels in the swimming trunk into the desired red color as

can be seen in the resultant images in Fig. 19(b) and (c), respec-tively. Both of the AJNDH and HA initialization schemes, on theother hand, manage to prevent themselves from suffering in suchclassification errors as shown in Fig. 19(d) and (e), respectively.

test image by various initialization schemes (b) randomly initialized (c) ACO, (d)

1844 K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852

F sults o(

Hbtoi

ettipT

FA

ig. 17. The image Fire Fighter; (a) original image, and the rest are segmentation red) AJNDH, and (e) HA.

owever, the proposed HA initialization scheme performs slightlyetter than the AJNDH initialization scheme as the proposed HA ini-ialization scheme is able to produce a more homogeneous regionn the swimmer’s leg, with less clusters as compared to the AJNDHnitialization scheme.

Finally, for the image Moon as illustrated in Fig. 20, it is inter-sting to see that there is an obvious classification error wherehe moon in the image has been falsely clustered to the sky byhe randomly initialized, ACO, and AJNDH initialization schemes

n Fig. 20(b)–(d) respectively, although some of them are able toroduce a more homogeneous background with fewer clusters.he proposed HA initialization scheme, on the other hand, has

ig. 18. The image Birds; (a) original image, and the rest are segmentation results of theJNDH, and (e) HA.

f the test image by various initialization schemes (b) randomly initialized (c) ACO,

successfully avoid this classification error by assigning the moonand sky as separate clusters as shown in Fig. 20(e).

Apart from the visual inspection results on those 7 images,an additional of 20 supplementary images are analyzed aswell to support the abovementioned findings. The findingsobtained from these 20 supplementary images are illustrated inFig. A.1 in Appendix A. Based on the visual inspection performedin Appendix A, it can be proven that the proposed HA initializa-tion scheme outperforms the randomly initialized, ACO, and AJNDH

initialization schemes as it is able to produce significantly bettersegmentation results, with more homogenous segmented regionsand less classification errors.

test image by various initialization schemes (b) randomly initialized (c) ACO, (d)

K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852 1845

F ults of the test image by various initialization schemes (b) randomly initialized (c) ACO,(

4

oitvcgdwsi

i

Table 2Number of cluster produced by different initialization schemes.

Images Initialization schemes

Randomly initialized ACO AJNDH HA

House 9 9 10 9Capsicums 15 15 14 15Nemo 14 9 13 14Fire Fighter 19 9 19 19Birds 8 3 3 8Swimmer 14 13 12 14Moon 8 3 3 8

FA

ig. 19. The image Swimmer; (a) original image, and the rest are segmentation resd) AJNDH, and (e) HA.

.2.2. Evaluation on cluster numberIn the qualitative results shown in the previous section, we

bserve that all of the randomly initialized, ACO, AJNDH, and HAnitialization schemes have their own unique mechanism to adap-ively initialize the cluster center distribution and the centroidalues. A good clustering result is highly dependent on the clusterenter initialization mechanism as a good initialization scheme canuarantee a high accuracy of classification and the advantage of lessistortion during the segmentation process. Thus, in this section,e are interested to know the relationship between the quality of

egmentation results and the number of cluster produced by each

nitialization scheme.

The number of cluster produced by each initialization schemes tabulated in Table 2. It is interesting to observe that the cluster

ig. 20. The image Moon; (a) original image, and the rest are segmentation results of theJNDH, and (e) HA.

Note: The bold values represent the best results obtained for the comparison.

test image by various initialization schemes (b) randomly initialized (c) ACO, (d)

1 Computing 13 (2013) 1832–1852

nseiciwspga

omtioTco(vt

piaca

Aripi(psActiist

boAdtofoecHaotHis

nt

Table 3Comparison of clustering quality among the proposed HA and other initializationschemes based on the MSE evaluation function.

Images Initialization schemes

Randomly initialized ACO AJNDH HA(*1.0e+2) (*1.0e+2) (*1.0e+2) (*1.0e+2)

House 3.1688 2.9670 2.7373 2.1728Capsicum 4.4297 4.4379 4.6439 4.0973Nemo 3.3309 3.8545 2.8995 2.4640Fire Fighter 2.7603 6.6132 2.7187 2.6126

4.2.4. Quantitative evaluation on segmentation resultsThe quantitative results obtained from the F(I), F′(I), and Q(I)

evaluation functions are tabulated in Tables 4–6 respectively. Fromthese tables, it can clearly be observed that the proposed HA

Table 4Comparison of segmentation results based the F(I) evaluation function.

Images Initialization schemes

Randomly initialized ACO AJNDH HA(*1.0e+2) (*1.0e+2) (*1.0e+2) (*1.0e+2)

House 4.3023 3.7738 2.6004 2.0706Capsicum 3.6407 3.6401 3.6861 3.3379Nemo 6.6320 5.4932 4.1116 3.3812

846 K.S. Tan et al. / Applied Soft

umber produced by each initialization scheme for every image isimilar, but not exactly the same. This observation is reasonable asach initialization scheme has their unique mechanism in decid-ng the cluster number. Meanwhile, we also can observed that theluster number produced by the randomly initialization schemes same as the proposed HA initialization scheme. This is because

e have made minor modification on the randomly initializationcheme, where the final cluster number is set to that obtained by theroposed HA initialization scheme. This minor modification coulduarantee the fair comparison between the randomly initializednd HA initialization schemes.

Another observation that should be highlighted is the possibilityf significant qualitative and quantitative differences in the seg-entation results produced by different algorithms despite having

he same cluster number. While the number of clusters produceds necessary, it is an insufficient performance metric to reveal theverall clustering performances of the aforementioned algorithms.he randomly initialized FCM and HA techniques have the sameluster number. However, Sections 4.2.3 and 4.2.4 show that thether performance metrics used to access the clustering qualityi.e. the MSE values) and homogeneity [i.e. the F(I), F′(I), and Q(I)alues] of the segmented images are significantly different amonghe randomly initialized FCM and HA technique.

As shown in Table 2, the proposed HA initialization schemeroduces less or comparable number of cluster than the randomly

nitialized, ACO, and AJNDH initialization schemes for image Housend Capsicums. Thus, by having smaller or comparable number ofluster, the proposed HA initialization scheme could produce largernd better homogenous regions in the segmented image.

Meanwhile, for images Birds and Moon, although the ACO andJNDH initialization schemes could produce larger homogenousegions by obtaining fewer number of cluster than the randomlynitialized and HA initialization schemes, there are considerableixels in the segmented images produced by the ACO and AJNDH

nitialization schemes which are falsely assigned to the backgroundi.e. sky), leading to the classification error problem. However, thisroblem has successfully avoided by the proposed HA initializationcheme, as the appropriate number of cluster has been obtained.lthough the randomly initialization scheme possess the sameluster number as the proposed HA initialization scheme, it suffershe same classification error as produced by the ACO and AJNDHnitialization schemes. This is due to the fact that the randomizednitialization mechanism possessed by the randomly initializationcheme, which has the unstable nature, does not properly initializehe initial cluster centers during the initialization stage.

As for image Nemo and Fire Fighter, although the cluster num-er produced by the proposed HA initialization scheme is morer comparable than those produced by the randomly initialized,CO, and AJNDH initialization schemes, the segmented results pro-uced by the proposed HA initialization scheme successfully avoidhe classification errors. Unlike the HA initialization scheme, thether compared initialization schemes have experienced the dif-erent level of classification errors, where there are certain amountf pixels in the segmented results are mistakenly clustered, asxplained in the previous section. Finally, for image Swimmer, theluster number produced by all the initialization schemes is similar.owever, the AJNDH and HA initialization schemes perform betters the severe classification error on the swimmer’s trunk could bebserved in the segmented images produced by the randomly ini-ialized and ACO initialization schemes. Furthermore, the proposedA initialization scheme performs slightly better than the AJNDH

nitialization scheme as it produces visually better quality of the

egmentation results than the AJNDH initialization scheme.

Based on the results tabulated in Table 2, we conclude that fewerumber of cluster does not always guarantee a good segmenta-ion results as there is a tradeoff between the number of cluster

Birds 0.7084 1.8408 1.8408 0.5244Swimmer 2.8028 2.9533 3.1334 2.6291Moon 2.7987 3.5934 3.5934 0.4167

produced and the quality of segmentation results. The insufficientnumber of cluster produced during the initialization stage tends tolead to the classification errors problems as shown in images Nemo,Fire Fighter, Birds, and Moon. Thus, instead of emphasizing the smallcluster number, we should keep a reasonable number of cluster andachieve more homogeneity within regions in order to obtain goodsegmentation results.

4.2.3. Evaluation on clustering qualityThe MSE values of the randomly initialized, ACO, AJNDH, and

HA initialization schemes are tabulated in Table 3. In Table 3, thebest results obtained are made bold while the second best are madebold and italic. This notation will be employed for the other resultspresented in this paper.

Based on Table 3, we can observe that the proposed HA initializa-tion scheme has exhibited its superior performance in term of theclustering quality over the other initialization schemes. The pro-posed HA initialization scheme always produces the smallest MSEvalues (i.e. ranked as the best), showing its capability in producingthe clustering results with less distortion as compared to the otherinitialization schemes. This observation is quite consistent with thevisual inspection as explained in Section 4.2.1.

Apart from the images as shown in Figs. 15–20, the MSE val-ues of the randomly initialized, ACO, AJNDH, and HA initializationschemes for another 20 supplementary images (as depicted inFig. A.1 in Appendix A) are tabulated in Table B.1 in Appendix B.Generally, the proposed HA initialization scheme outperformsthe randomly initialized, ACO, and AJNDH initialization schemesby consistently producing the relatively smaller MSE values (i.e.ranked as the best or second best) in those 20 images. The capabilityof the proposed HA initialization scheme to consistently producethe smaller MSE values successfully proves its advantage in pro-ducing the clustering results with better cluster distribution ascompared to the other initialization schemes.

Fire Fighter 5.0150 13.7404 4.2908 4.2477Birds 1.3315 4.7516 4.7516 1.3098Swimmer 3.7584 4.0451 4.2976 3.6715Moon 2.5424 2.9085 2.9085 1.5595

K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852 1847

Table 5Comparison of segmentation results based on the F′(I) evaluation function.

Images Initialization schemes

Randomly initialized ACO AJNDH HA(*1.0e+1) (*1.0e+1) (*1.0e+1) (*1.0e+1)

House 4.3922 3.8584 2.6542 2.1257Capsicum 3.7269 3.7253 3.7752 3.4248Nemo 6.7685 5.6448 4.2101 3.4610Fire Fighter 5.0397 13.8679 4.3126 4.2737

ivWtQosthrot

figFegTtAIberdabboNcpste

Ap

TC

Table 7Performance comparison of segmentation results based on average values of MSE,F(I), F′(I), and Q(I) for 140 standard images.

Initialization schemes Benchmark quantitative evaluation functions

MSE F(I) F′(I) Q(I)(*1.0e+2) (*1.0e+2) (*1.0e+1) (*1.0e+5)

Randomly initialized 3.1900 7.3500 7.4400 0.6890ACO 3.5200 8.5300 8.6600 0.5710

Birds 1.3499 4.9124 4.9124 1.3299Swimmer 3.8453 4.1389 4.4134 3.7577Moon 2.5758 3.0569 3.0569 1.5864

nitialization scheme produces the best (smallest) F(I), F′(I), and Q(I)alues for the image House, Capsicums, Birds, Swimmer, and Moon.hile for images Nemo and Fire Fighter, the proposed HA initializa-

ion scheme produces the best F(I) and F′(I) values and second best(I) value. These results support the promising qualitative findingsbtained by the proposed HA initialization scheme in the previousection as the smaller values of F(I), F′(I), and Q(I) evaluation func-ions tend to produce good segmentation results, which have moreomogenous and less distortion segmented regions. Thus, theseesults strongly prove that the proposed HA initialization schemeutperforms the randomly initialized, ACO, and AJNDH initializa-ion schemes both qualitatively and quantitatively.

Meanwhile, another important finding that could be observedrom the results tabulated in Tables 4–6 is that the other initial-zation schemes that have been put in comparison could produceood F(I), F′(I), and Q(I) evaluation functions for only certain images.or example, the ACO initialization scheme produces the small-st Q(I) value for image Fire Fighter but fails to produce the sameood result (i.e. small values of Q(I)) for images Birds and Capsicums.he similar findings could be observed for other evaluation func-ions (i.e. F(I) and F′(I)) on other images. Similarly, the ACO andJNDH initialization schemes also suffer with the same problem.

n addition, we also observe that the good performance achievedy these compared initialization schemes in the F(I), F′(I), and Q(I)valuation functions is not always consistent with the qualitativeesults as presented in Section 4.3.1. For example, although the ran-omly initialization scheme could produce second best F(I), F′(I),nd Q(I) values in image Birds, a significant classification error coulde observed in the segmented image as the white feather of theirds is falsely clustered into the sky. Similar problems could bebserved on the segmentation results of images Swimmer, Moon,emo, Fire Fighter produced by the ACO initialization scheme. Inontrary, although the F(I), F′(I), and Q(I) values produced by theroposed HA initialization scheme are also relatively small, it hasuccessfully exhibited its robustness in preserving the salient fea-ures of the input color images as well as prevents the classificationrrors during the segmentation process.

Finally, it is also observed that the randomly initialized, ACO, andJNDH initialization schemes produce inconsistent quantitativeerformance (i.e. based on the F(I), F′(I), and Q(I) values obtained)

able 6omparison of segmentation results based on the Q(I) evaluation function.

Images Initialization schemes

Randomly initialized ACO AJNDH HA(*1.0e+3) (*1.0e+3) (*1.0e+3) (*1.0e+3)

House 0.7716 0.7056 0.3495 0.2813Capsicum 0.5653 0.5740 0.5347 0.4776Nemo 6.1464 0.7001 2.1969 1.8929Fire Fighter 348.4360 28.1336 317.0170 172.0360Birds 0.3868 2.0572 2.0572 0.3803Swimmer 0.5075 0.5449 0.5813 0.5073Moon 1.7599 1.3058 1.3058 0.7068

AJNDH 3.2200 7.7900 7.8900 1.2400HA 2.9000 6.8400 6.9200 0.5690

for the same image. For example, the ACO initialization schemeproduces the best Q(I) value for the image Fire Fighter but achievesthe worst ranking in terms of the F(I) and F′(I) values. The sameproblems can also be observed for the randomly initialized andAJNDH initialization schemes. On the other hand, the proposedHA initialization scheme can perform consistently, by producingthe relatively small F(I), F′(I), and Q(I) evaluation functions for allimages. This successfully proves the ability of the proposed HA ini-tialization scheme in persisting consistent and good performancefor any type of analyses and images.

In order to support the abovementioned findings, the F(I),F′(I), and Q(I) values of the randomly initialized, ACO, AJNDH,and HA initialization schemes for another 20 supplementaryimages (as depicted in Fig. A.1 in Appendix A) are tabulated inTable C.1 in Appendix C. Overall, notice from the quantitativeresults of F(I), F′(I), and Q(I) values as shown in Table C.1, it is clearlyshown the proposed HA initialization scheme produces relativelysmaller values in these three evaluation benchmarks as comparedto the other compared initialization schemes. Thus, the segmenta-tion results produced by the proposed HA initialization scheme aremore favored. Although both of the ACO and AJNDH initializationschemes could produce smaller values of F(I), F′(I), and Q(I) than theproposed HA initialization scheme in certain images, the differencein these values is not significant, and furthermore the segmentationregions produced by the proposed HA initialization scheme is morehomogenous and less distortion as compared to other initializationschemes when inspected visually.

Meanwhile, it is also worth to point out that the randomlyinitialization scheme could achieve slightly good performance incertain images as it is able to produce comparable F(I), F′(I), andQ(I) values with the proposed HA initialization scheme. The excel-lence performance of the randomly initialization scheme in certainimages is mainly due to the fact that both of the randomly initial-ized and HA initialization schemes are sharing the same clusternumber during the segmentation process. However, the randomlyinitialization scheme fails to maintain its consistent performancesfor all images as the randomized mechanism that involved dur-ing the initialization process of the cluster center is unstable andhas too much uncertainties involved. This could lead to less sat-isfactory initialization of cluster centers, which is then followedby a poor segmentation result. On the other hand, for the proposedHA initialization scheme, the abovementioned unstable nature anduncertainties issues during the initialization stage do not exist as itoffers a more systematic procedure of splitting and merging mod-ules to initialize the cluster center. Such systematic procedure canguarantee a more accurate and reasonable estimation of the ini-tial cluster, and this ensures the proposed HA initialization schemecould persist its outstanding performance for all images.

To further evaluate the segmentation results produced by theproposed HA initialization scheme and the other state-of-art initial-ization schemes, the average value of MSE, F(I), F′(I), and Q(I) for 140

natural images taken from the public segmentation database aregiven as tabulated in Table 7. As shown in Table 7, the results clearlyprove that the proposed HA initialization scheme successfully

1 Compu

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schemes based on the F(I), F (I) and the Q(I) evaluation

848 K.S. Tan et al. / Applied Soft

utperforms the randomly initialized, ACO, and AJNDH initializa-ion schemes by producing the smallest average values of MSE, F(I),′(I), and Q(I). This is then followed by the randomly initialized andJNDH initialization schemes. The ACO initialization scheme, on

he other hand, produces the worst results by producing the largestalues of MSE, F(I), and F′(I), and large value of Q(I). Based on theverage MSE values shown, we can conclude that the proposed HAnitialization scheme is able to generate a more compact and sta-le cluster during the clustering process as compared to the other

nitialization schemes. Furthermore, the outstanding capabilitiesf the proposed HA initialization scheme in consistently produc-ng the small values of F(I), F′(I), and Q(I) during the segmentationrocess suggesting the potential of the proposed HA initializationcheme to be employed as a robust and excellence initializationcheme for the conventional FCM algorithm.

. Conclusions

In this paper, the HA initialization scheme is proposed to over-ome the sensitiveness of FCM algorithm to the initializationondition of clusters number and initial cluster centers as they haveignificant impacts on the segmentation quality. In other word, bet-er segmentation result could be achieved if better initializationondition for FCM algorithm is provided. From the experimen-al results, it can be concluded that the proposed initializationcheme could produce better initialization condition for FCM algo-ithm than the randomly initialized, ACO and AJNDH initializationchemes by successfully reducing the classification errors and pro-ucing more homogeneous regions in the segmentation results.eanwhile, the quantitative analysis also proves that the pro-

osed HA initialization scheme has successfully produced betteregmentation results. Thus, it is recommendable for this algorithmo be applied in the post image processing in consumer electronicroducts or machine vision systems, which are, for example, exten-ively used with the microscope in capturing microscopic images,specially in segmenting medical images. As future work, we willnvestigate the impact of different color conversion technique onhe clustering results. More specifically, the newly proposed HSLolor space such as those proposed in [25] will be employed in ourA module to determine whether the clustering results will change

ignificantly when different variants of HSL color space is used. Inddition, we also like to further investigate the capability of theA initialization scheme to perform segmentation with other per-

ormance metrics such as the F-measure, variation of information,and index as adopted by the literatures in [49,50].

cknowledgements

The authors would like to express their sincere thanks to thessociate editor and all reviewers who made great contributions to

ting 13 (2013) 1832–1852

the improvement of the final paper. This research was supportedby the Fundamental Research Grant Scheme (FRGS) entitled “Inves-tigation of New Color Image Illumination Estimation Concept forDevelopment of New Color Correction Techniques” and UniversitiSains Malaysia (USM) Postgraduate Fellowship Scheme.

Appendix A. Segmentation results of the 20 test images bythe randomly initialized, ACO, AJNDH, and HA initializationschemes

Fig. A1.

Appendix B. Comparison of segmentation results by therandomly initialized, ACO, AJNDH, and HA initializationschemes based on the MSE evaluation function

Table B1.

Table B1Comparison of clustering quality based on the MSE evaluation function.

Test Image Initialization schemes

Randomly initialized AFHA AJNJDH RFHA(*1.0e+2) (*1.0e+2) (*1.0e+2) (*1.0e+2)

MSE

Diver 1 1.8738 6.7123 1.6425 1.5621Crown 2.1728 3.1039 3.0312 2.2799Car 2.4405 3.5353 2.4405 2.5226Cow 3.0375 3.0375 2.2997 3.0375Insect 2.3378 2.7968 4.8237 2.2173White Church 1.8040 2.4351 1.8225 1.7999Beach 2.8764 2.9097 2.6842 2.6842Red Church 1.4772 2.3447 1.7596 1.4648Pyramid 5.7642 4.7869 3.9997 3.4171Drum Players 0.4690 0.2561 0.2843 0.2843Statues 1.2196 2.2036 1.8679 1.2064Eagle 3.0806 3.8248 3.8248 3.0806White Boat 4.7628 4.8270 3.2343 3.6140Diver 3.0049 2.6116 2.9407 2.9407Island 2.2623 3.9973 2.2623 2.1480Cactus 3.5109 3.1634 3.7046 3.1634Horses 3.2572 2.8643 3.5025 3.1542Building 3.6886 4.8967 4.2599 3.6699Onion 2.6336 2.5814 3.5940 2.5768Pegion 2.1085 4.0238 2.4239 2.2026

Appendix C. Comparison of segmentation results by therandomly initialized, ACO, AJNDH, and HA initialization

′

functions

Table C1.

K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852 1849

Fig. A1. Image segmentation results. First column: images’ name. Second column: the original image. Third column: the randomly initialization scheme segmentation.Fourth column: the ACO initialization scheme segmentation. Fifth column: the AJNDH initialization scheme segmentation. Sixth column: the proposed HA initilizationscheme segmentation.

1850 K.S. Tan et al. / Applied Soft Computing 13 (2013) 1832–1852

Fig. A1. (Continued).

K.S. Tan et al. / Applied Soft Compu

Table C1Comparison of segmentation results based on the F(I), F′(I), and Q(I) evaluationfunctions.

Test Image Initialization schemes

Randomly initialized AFHA AJNJDH RFHA(*1.0e+3) (*1.0e+3) (*1.0e+3) (*1.0e+3)

F(I)

Diver 1 0.2543 1.5562 0.2899 0.2279Crown 0.9769 1.4722 1.4175 0.9768Car 0.2244 0.2942 0.2112 0.1896Cow 0.8379 0.8379 0.5235 0.8379Insect 0.2892 0.4287 0.8857 0.2753White Church 0.3746 0.6051 0.3890 0.3522Beach 0.2445 0.2366 0.2216 0.2216Red Church 0.3295 0.4609 0.3659 0.3192Pyramid 1.0677 0.8503 1.2122 1.0512Drum Players 0.9319 0.5079 0.5763 0.5763Statues 0.1979 0.7893 0.3427 0.2024Eagle 0.2683 0.5713 0.4073 0.2598White Boat 0.9049 1.1161 1.1161 0.9049Diver 2 1.12299 1.3849 0.6832 0.7903Island 0.8632 0.8196 0.8457 0.8456Cactus 0.3576 0.7225 0.3415 0.2950Horses 1.00617 0.7023 1.0401 0.7023Building 1.0406 0.7814 1.1187 0.9126Onion 0.1613 0.1979 0.1859 0.1723Pegion 0.5044 0.5036 0.8647 0.4767

Image Initialization schemes

Randomly initialized AFHA AJNJDH RFHA(*1.0e+2) (*1.0e+2) (*1.0e+2) (*1.0e+2)

F′(I)

Diver 1 0.2579 1.6031 0.2947 0.2313Crown 0.9870 1.4918 1.4367 0.9870Car 0.2286 0.3028 0.2158 0.1934Cow 0.8463 0.8463 0.5272 0.8463Insect 0.2973 0.4397 0.9079 0.2814White Church 0.3818 0.6176 0.3961 0.3581Beach 0.2510 0.2443 0.2280 0.2280Red Church 0.3336 0.4673 0.3713 0.3230Pyramid 1.2559 1.0062 0.9935 0.5532Drum Players 0.9368 0.5111 0.5806 0.5806Statues 0.2714 0.5800 0.4125 0.2628Eagle 0.9179 1.1322 1.1322 0.9179White Boat 1.1287 1.3957 0.6867 0.7944Diver 2 0.8814 0.8344 0.8634 0.8632Island 0.3599 0.7337 0.3442 0.2974Cactus 1.0190 0.7129 1.0555 0.7127Horses 1.0534 0.7906 1.1340 0.9238Building 0.1672 0.2061 0.1935 0.1784Onion 0.5138 0.5134 0.8879 0.4860Pegion 0.7412 1.3732 0.8211 0.6590

Image Initialization schemes

Randomly initialized AFHA AJNJDH RFHA(*1.0e+3) (*1.0e+3) (*1.0e+3) (*1.0e+3)

Q(I)

Diver 1 1.0157 3.8594 0.8117 0.7672Crown 3.7284 4.0840 3.9176 2.8727Car 0.3986 0.3948 0.3238 0.3109Cow 10.9058 10.9058 47.7409 10.9058Insect 0.4826 0.6261 1.5019 0.5788White Church 0.7637 1.5202 0.8091 0.6961Beach 0.2959 0.2847 0.2645 0.2645Red Church 0.9074 1.0013 0.9044 0.8755Pyramid 3.5723 1.6213 3.3046 1.4464Drum Players 218.3890 121.7550 65.2754 65.3106Statues 1.7088 1.7838 1.1837 1.6753Eagle 2.4176 2.3296 2.3296 2.4164White Boat 284.5980 34.5471 256.8220 22.31620Diver 2 1.6661 1.6824 1.6557 1.6552Island 134.7760 2.5992 61.2981 52.8101Cactus 6.4033 2.9239 3.7440 2.9239Horses 3.4558 3.0736 2.9547 2.7117Building 0.1156 0.1523 0.1467 0.1459Onion 1.5045 1.4099 1.7085 1.3253Pegion 4.634.8 2.9134 2.8578 2.6959

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Khang Siang Tan received his B. Eng. degree in Mechatronic Engineering from Uni-versiti Sains Malaysia (USM), Malaysia in the year 2009. In year 2011, he receivedhis M.Sc. degree in Electrical and Electronic Engineering from the same univer-sity. During his time in pursuing his M.Sc. degree, he was attached to the Imagingand Intelligent Systems Research Team (ISRT), School of Electrical and ElectronicEngineering, USM. His research interests include image enhancement and imagesegmentation.

Wei Hong Lim received his B. Eng. degree in Mechatronic Engineering with FirstClass Honors from USM, Malaysia in the year 2011. He is currently pursuing his Ph.D.degree in Electrical and Electronic Engineering and is attached to the Imaging andIntelligent System Research Team (ISRT), School of Electrical and Electronic Engi-neering, USM. His research interests include digital image processing and artificialintelligent.

Nor Ashidi Mat Isa received the B. Eng. degree in Electrical and Electronic Engineer-ing with First Class Honors from USM in 1999. In 2003, he went on to receive hisPh.D. degree in Electronic Engineering (majoring in Image Processing and ArtificialNeural Network). He is currently an Associate Professor and lecturing at the School

gent systems, image processing, neural network, biomedical engineering, intelligentdiagnostic systems and algorithms. As of now, he has led his ISRT research group topublish at both national and international arena. Their contributions can be foundin numerous journals, chapters in books and proceedings.